I live in Brisbane and am always encouraging visitors to see Stradbroke Island if they are coming to our part of the world. It's not for everyone (there's limited night life or shopping for example), but if you want beautiful unspoilt beaches, safe swimming for kids, and interesting walks then this is the place.
Straddy is best done by car and car ferry, but it is possible by public transport (train to Cleveland, bus to water taxi, water taxi, bus at the other end to Point Lookout). Car ferries run pretty much hourly from Cleveland. There are two operators - Stradbroke Ferries and the Big Red Cat. Both are the same price (about $120 return).
There are quite a few accommodation options at Point Lookout. If you search accommodation you will find a few resorts, but the cheaper option if you have time is to rent a house for a week via one of the main real estate agents - Dolphin or The Accommodation Centre. Both have pretty good web sites with houses that can be booked on line.
We aim to stay near to Cylinder Beach (the safest for kids) or Deadmans Beach (nicest walks).